SOLUTION: Hello! Please help me solve this composite function. What is g(f(x))where f(x)= 1/SQURT x-3 and g(x)= 2/x+1? I am able to plug in f(x) into g to get 2/(1/SQURT x-3)+1 but then get

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Question 286540: Hello! Please help me solve this composite function. What is g(f(x))where f(x)= 1/SQURT x-3 and g(x)= 2/x+1? I am able to plug in f(x) into g to get 2/(1/SQURT x-3)+1 but then get stuck with the algebra. How do I simplify this? I turned (1) into root of (x-3)/root of (x-3) to establish a common denominator but am not seeing how to get the answer which my book says is 2/(root of x-3)+1. Thank you in advance for your help :)
Answer by dabanfield(803) (Show Source):
You can put this solution on YOUR website!
Hello! Please help me solve this composite function. What is g(f(x))where f(x)= 1/SQURT x-3 and g(x)= 2/x+1? I am able to plug in f(x) into g to get 2/(1/SQURT x-3)+1 but then get stuck with the algebra. How do I simplify this? I turned (1) into root of (x-3)/root of (x-3) to establish a common denominator but am not seeing how to get the answer which my book says is 2/(root of x-3)+1. Thank you in advance for your help :)
Great start! :)
Note that sqrt(x-3)/sqrt(x-3) = 1 so:
2/(1/(sqrt(x-3)) + 1) =
2/(1/sqrt(x-3) + sqrt(x-3)/sqrt(x-3)) =
2/((1+sqrt(x-3))/sqrt(x-3)
Multiply numerator and denominator by sqrt(x-3):
(2*sqrt(x-3))/(1 + sqrt(x-3))
This isn't what you said the book had for the solution though.